Philosophy and Time
Quine, from Word and Object (reprinted in Westphal, ed.)
A dense and meaty selection from a dense and meaty book. (It's from section 36 of Word and Object, in case you were wondering.)
1. recommendation: get rid of tense; construe the grammatical present tense as temporally neutral, and convey temporal information by explicit reference to times. So "I will not do it again" → "I do not do it after now." "After now" in turn is understood by analogy to "west of here."
sometimes we already regard the present tense as temporally neutral, e.g. in "seven is an odd number."
And tensed verbs force us to at least apparently include information about tense even when it is not relevant.
2. This will clarify some arguments.
1. Seven of them remained.
2. Seven is an odd number.
3. An odd number of them remained.
That's a valid argument, but appears to have exactly the same form as:
1. George married Mary.
2. Mary is a widow.
3. George married a widow.
Alas for poor George, this second argument is clearly not valid. Reformulating the argument in accordance with Quine's recommendation, we obtain:
1. George marries Mary before now.
2. Mary is a widow now.
3. George marries before now (one who is) a widow now.
which is valid, but leads to a different conclusion. (Or if we keep the conclusion the same, "3. George marries before now one who is a widow before now," the argument is clearly invalid.)
3. Objects (including people) have temporal parts as well as spatial parts. This helps with Heraclitus' problem about stepping into the same river twice. It also clarifies issues about personal identity: there doesn't need to be an essence of me that remains constant over time any more than there needs to be an essence of me that remains constant from one part of my body to another. (Not that there couldn't be such an essence, e.g. the structure of DNA in the cells of these various parts, just that there need not be.)
4. Interesting: if we think of objects as four-dimensional, then there is no longer a distinction between objects, events, and processes. Each is "simply the content . . . of some portion of space-time."
5. A time (say, 2:30 - 3:45 on 10-8-2003) is a slice of the 4D world. Then "x at t" should be understood to mean "the common part of x and t." So CB at the time above chops off all parts of me that are earlier or later, and everything at that time that isn't part of me: it's the intersection of me and t. (Not technically the intersection, because intersection applies to sets rather than objects, but the mereological counterpart of intersection -- the overlap of me and t.)
6. Before and after as relative terms. "x is eating y before t" → ∃u (u is before t & x at u is eating y).